In the production of gears, especially bevel gears, two types of processes are commonly employed, generating processes and non-generating processes.
Generating processes can be divided into two categories, face milling (intermittent indexing) and face hobbing (continuous indexing). In generating face milling processes, a rotating tool is fed into the workpiece to a predetermined depth. Once this depth is reached, the tool and workpiece are then rolled together in a predetermined relative rolling motion, known as the generating roll, as though the workpiece were rotating in mesh with a theoretical generating gear, the teeth of the theoretical generating gear being represented by the stock removing surfaces of the tool. The profile shape of the tooth is formed by relative motion of the tool and workpiece during the generating roll.
In generating face hobbing processes, the tool and workpiece rotate in a timed relationship and the tool is fed to depth thereby forming all tooth slots in a single plunge of the tool. After full depth is reached, the generating roll is commenced.
Non-generating processes, either intermittent indexing or continuous indexing, are those in which the profile shape of a tooth on a workpiece is produced directly from the profile shape on the tool. The tool is fed into the workpiece and the profile shape on the tool is imparted to the workpiece. While no generating roll is employed, the concept of a theoretical generating gear in the form of a theoretical “crown gear” is applicable in non-generating processes. The crown gear is that theoretical gear whose tooth surfaces are complementary with the tooth surfaces of the workpiece in non-generating processes. Therefore, the cutting blades on the tool represent the teeth of the theoretical crown gear when forming the tooth surfaces on the non-generated workpiece.
The relationship between the workpiece and generating gear can be defined by a group of parameters known as basic machine settings. These basic settings communicate a sense of size and proportion regarding the generating gear and the workpiece and provide a common starting point for gear design thus unifying design procedures among many models of machines. The basic settings totally describe the relative positioning between the tool and workpiece at any instant.
Basic machine settings for forming gears are known in the art and may be defined as follows:                1. cradle angle (q) which defines the angular position of the tool about the cradle axis;        2. radial setting (S) which is the distance between the cradle axis and the tool axis;        3. swivel angle (j) which defines the orientation of the tool axis relative to a fixed reference on the cradle;        4. tilt angle (i) which defines the angle between the cradle axis and the tool axis;        5. root angle (ym) which sets forth the orientation of the work support relative to the cradle axis;        6. center-to-back or head setting (Xp) which is a distance along the work axis from the apparent intersection of the work and cradle axes to a point located a fixed distance from the workpiece;        7. work offset (Em) which defines the distance between the work axis and the cradle axis;        8. sliding base (Xb) which is the distance from the machine center to the apparent intersection of the work and cradle axes;        9. rotational position of the workpiece (ωw);        10. rotational position of the tool (ωt), for face hobbing;        11. ratio-of-roll (Ra) between cradle rotation and workpiece rotation, for generating.        
In conventional gear forming machines, the cradle angle, workpiece rotation and tool rotation change during generation while the other settings generally remain fixed. Two notable exceptions to this are helical motion which involves motion of the sliding base, Xb, and vertical motion which is motion on the work offset direction, Em.
The conventional mechanical machine meets the concept of the theoretical basic machine since nearly all machine settings correspond to theoretical basic settings. Such a machine is illustrated by FIG. 4. In the mechanical machine, the basic setting for the radial, S, is controlled by an angular machine setting known as the eccentric angle.
Generating and non-generating processes are usually carried out on conventional mechanical gear generating machines or on rectilinear multi-axis computer controlled (e.g. CNC) gear generating machines (such machines also being known as “free-form” machines). Conventional mechanical gear generating machines for producing bevel gears comprise a work support mechanism and a cradle mechanism. During a generating process, the cradle carries a circular tool along a circular path about an axis known as the cradle axis. This is known as the generating roll or cradle roll. The cradle represents the body of the theoretical generating gear and the cradle axis corresponds to the axis of the theoretical generating gear. The tool represents one or more teeth on the generating gear. The work support orients a workpiece relative to the cradle and rotates it at a specified ratio to the cradle rotation. Traditionally, conventional mechanical cradle-style bevel gear generating machines are usually equipped with a series of linear and angular scales (i.e. settings) which assist the operator in accurately locating the various machine components in their proper positions.
It is common in many types of conventional mechanical cradle-style bevel gear generating machines to include an adjustable mechanism which enables tilting of the cutter spindle, and hence, the cutting tool axis, relative to the axis of the cradle (i.e. the cutter axis is not parallel to the cradle axis). Known as “cutter tilt,” the adjustment is usually utilized in order to match the cutting tool pressure angle to the pressure angle of the workpiece, and/or to position the cutting surfaces of the tool to appropriately represent the tooth surfaces of the theoretical generating gear. In some types of conventional mechanical cradle-style bevel gear generating machines without a cutter tilt mechanism, the effects of cutter tilt may be achieved by an altering of the relative rolling relationship between the cradle and workpiece. This altering is also known as “modified roll.” (only for fixed setting)
In multi-axis computer controlled gear generating machines, such as those disclosed by U.S. Pat. Nos. 4,981,402; 6,669,415 and 6,712,566, the disclosures of which are hereby incorporated by reference, movement of a tool relative to a workpiece along or about multiple machine axes (e.g. 5 or 6) can perform the cycle of movements including the kinematical relationship of the work and tool in the manner the same (or nearly the same) as that performed to generate a bevel gear in a conventional machine process utilizing a known face mill cutter or grinding wheel.
It has generally become the practice in the art to utilize the same input parameters (e.g. machine settings) as a conventional mechanical cradle-style gear generating machine for multi-axis computer controlled gear generating machines having a different number and/or configuration of axes. In other words, the positions of the tool and workpiece axes in the coordinate system of a conventional mechanical cradle-style bevel gear generating machine are transformed into the alternative coordinate system of the multi-axis computer controlled gear generating machine. Examples of such transformations can be found in the above referenced U.S. Pat. Nos. 4,981,402; 6,669,415 and 6,712,566, the disclosures of which are hereby incorporated by reference.
Bevel and hypoid gears which are cut in a continuous indexing process (face hobbing) have generally a parallel tooth depth along the face width. A basic cutting setup in the generating or cradle plane will put the center of the cutter head in a position which is away from the generating gear center (cradle axis) by an amount commonly referred to as the radial distance. The cutter head axis is parallel to the generating gear or cradle axis. A gear blank can be positioned in front of the cradle and the cutter, such that the cutter blades will cut the gear slots. The cutting edges of the basic cutting setup are straight in order to resemble the generating gear profile. While the cutter rotates, the gear will have to rotate during each cutter revolution by as many pitches, as the cutter has starts (blade groups). In order to generate the profile form of the gear teeth, the generating gear has to rotate about its axis, while the gear rotates by the generating gear rotation angle multiplied by the ratio of roll. The ratio of roll is the number of generating gear teeth divided by the number of work gear teeth.
A mating pinion to the described gear is cut and generated the same way. However, if the gear was generated with the cutter head center above the center of the generating gear (right hand spiral), then the pinion has to be generated with the cutter center below the center of the generating gear (left hand spiral). Pinion and gear generated in this manner will have an epicyclic flank line and on octoide tooth profile. Since both members are generated with mirror images of the generating gear, they will roll together perfectly conjugate. This means pinion and gear contact each other along contact lines which extend over the entire active flank surface. In a theoretical environment, pinion and gear will roll without motion error and have a full flank contact.
Gears produced for practical applications require a located flank contact in order to allow for load affected deflections of gearbox, shafts, gear bodies and teeth. In particularly for large gears, a crowning in profile (i.e. tooth height) direction and a crowning in face width (i.e. tooth lengthwise) direction is applied to both members. The crowning in profile direction is generally accomplished by changing the straight cutting edge profile of the cutting blades to a concave curve. Pinion and gear blades preferably receive the same radius of curvature such that each of them contributes to 50% of the profile crowning.
The crowning in the length direction for gears up to a ring gear diameter of about 800 mm is generally accomplished by inclination of the cutter head (i.e. cutter tilt). The cutter head inclination is arranged such that the original spiral angle and tooth slot proportions in the center of the teeth remain constant. Deeper cutting towards the ends will make the tooth slots wider towards the ends thereby creating a crowning in face width direction.
In bevel gear sets with a ring gear diameter above 800 mm it becomes difficult to realize a provision in a mechanical machine to tilt a cutter head in space. If the manufacturing machine is a 6-axis numerically controlled free form machine, then the cutter tilt is converted into an interpolating motion of the pivot axis (e.g. U.S. Pat. No. 4,981,402 discussed above). In case of such large gears it has been found that it is also difficult to realize such a highly precise interpolating motion of a machine component which can weigh several tons. Consequently, all dedicated large bevel gear manufacturing machines avoid the principle of a tilted cutter. As a consequence, the required length crowning is generated by slightly changing the radii of the cutting blade location relative to the cutter head axis. In some cases, for example, it is sufficient if the radial location of the inside blades of pinion and gear cutter is reduced by about 1% of the nominal cutter radius. The inside blades will generate a circular stock off condition moving from the center of the teeth to the inner or outer end of the teeth. The modified convex pinion flanks mesh with the unmodified concave gear flanks and the modified convex gear flanks mesh with the unmodified concave pinion flanks. This interaction will provide the desired amount of crowning in face width direction in both rotational directions of the gearset.
Outside and inside blades of a face hobbing cutter head initially have, before a radius modification is introduced, the same radius at the blade reference point. The continuous indexing motion rotates the work by the angular slot width after the first blade (e.g. outside blade) of one blade group passes a certain point along the face width until the second blade of the same blade group (e.g. inside blade) passes the same point within the same slot. If the radii of the inside blades are reduced in order to generate length crowning, then the produced slot width will be too large. As a consequence, there are two methods to cut the correct slot width:                (a) First setup for cutting convex flanks and second setup for cutting concave flanks        (b) Two interlocking face cutters connected to two different spindle connections on cutting machine        
Method (a) requires two different cutting machine setups and two separate cutting cycles. Method (b) requires a complex “second spindle in the first spindle” arrangement, where the second spindle requires an eccentricity offset versus the first spindle which also requires a provision for correct angular orientation in the generating gear plane. Method (b) reduces the machine stiffness and therefore requires small generating roll rates (compared to a single cutter-spindle connection). All large face hobbed gears, which require cutter head diameters above 210 mm are manufactured according to method (a). Method (a) requires nearly twice the cutting time than that of a conventional completing process.
A cutter radius modification therefore prevents a completing cutting process for large gears. A cutter head tilt will activate in numerically controlled machines an interpolating swing angle (root angle) motion during the entire generating process. Although this would still allow a completing process, the interpolating (coupled) rotation of only fractional degree amounts of a machine component with the weight of several tons will reduce process stiffness and accuracy and also be very costly in its mechanical realization.
A face hobbing or face milling cutting method which performs a completing cutting process that generates the desired amounts of length crowning requires either a cutter radius modification or an interpolating swing axis motion. For a productive completing process of manufacturing bevel gears with a ring gear diameter above about 800 mm, cutter radius modifications will not be reasonably possible and a cutter head tilt (equal to an interpolating swing (pivot) axis motion in free form machine) reduces process stiffness and therefore reduces productivity and accuracy. The present invention presents a solution to overcome these and other deficiencies.